Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,10,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(101.462059724\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −25.4393 | −1.12427 | −0.562135 | − | 0.827045i | \(-0.690020\pi\) | ||||
−0.562135 | + | 0.827045i | \(0.690020\pi\) | |||||||
\(3\) | 83.7395 | 0.596877 | 0.298438 | − | 0.954429i | \(-0.403534\pi\) | ||||
0.298438 | + | 0.954429i | \(0.403534\pi\) | |||||||
\(4\) | 135.160 | 0.263984 | ||||||||
\(5\) | −347.412 | −0.248588 | −0.124294 | − | 0.992245i | \(-0.539667\pi\) | ||||
−0.124294 | + | 0.992245i | \(0.539667\pi\) | |||||||
\(6\) | −2130.28 | −0.671051 | ||||||||
\(7\) | 1070.50 | 0.168517 | 0.0842587 | − | 0.996444i | \(-0.473148\pi\) | ||||
0.0842587 | + | 0.996444i | \(0.473148\pi\) | |||||||
\(8\) | 9586.56 | 0.827481 | ||||||||
\(9\) | −12670.7 | −0.643738 | ||||||||
\(10\) | 8837.93 | 0.279480 | ||||||||
\(11\) | −65986.5 | −1.35890 | −0.679451 | − | 0.733721i | \(-0.737782\pi\) | ||||
−0.679451 | + | 0.733721i | \(0.737782\pi\) | |||||||
\(12\) | 11318.2 | 0.157566 | ||||||||
\(13\) | 13095.3 | 0.127166 | 0.0635828 | − | 0.997977i | \(-0.479747\pi\) | ||||
0.0635828 | + | 0.997977i | \(0.479747\pi\) | |||||||
\(14\) | −27232.8 | −0.189459 | ||||||||
\(15\) | −29092.1 | −0.148376 | ||||||||
\(16\) | −313078. | −1.19430 | ||||||||
\(17\) | −376745. | −1.09403 | −0.547013 | − | 0.837124i | \(-0.684235\pi\) | ||||
−0.547013 | + | 0.837124i | \(0.684235\pi\) | |||||||
\(18\) | 322334. | 0.723736 | ||||||||
\(19\) | 294947. | 0.519222 | 0.259611 | − | 0.965713i | \(-0.416406\pi\) | ||||
0.259611 | + | 0.965713i | \(0.416406\pi\) | |||||||
\(20\) | −46956.1 | −0.0656232 | ||||||||
\(21\) | 89643.0 | 0.100584 | ||||||||
\(22\) | 1.67865e6 | 1.52777 | ||||||||
\(23\) | 1.95882e6 | 1.45955 | 0.729774 | − | 0.683688i | \(-0.239625\pi\) | ||||
0.729774 | + | 0.683688i | \(0.239625\pi\) | |||||||
\(24\) | 802774. | 0.493904 | ||||||||
\(25\) | −1.83243e6 | −0.938204 | ||||||||
\(26\) | −333135. | −0.142969 | ||||||||
\(27\) | −2.70928e6 | −0.981109 | ||||||||
\(28\) | 144688. | 0.0444859 | ||||||||
\(29\) | −6.45398e6 | −1.69448 | −0.847240 | − | 0.531211i | \(-0.821737\pi\) | ||||
−0.847240 | + | 0.531211i | \(0.821737\pi\) | |||||||
\(30\) | 740083. | 0.166815 | ||||||||
\(31\) | −2.48027e6 | −0.482360 | −0.241180 | − | 0.970480i | \(-0.577534\pi\) | ||||
−0.241180 | + | 0.970480i | \(0.577534\pi\) | |||||||
\(32\) | 3.05617e6 | 0.515231 | ||||||||
\(33\) | −5.52568e6 | −0.811097 | ||||||||
\(34\) | 9.58415e6 | 1.22998 | ||||||||
\(35\) | −371904. | −0.0418914 | ||||||||
\(36\) | −1.71257e6 | −0.169937 | ||||||||
\(37\) | 9.56186e6 | 0.838754 | 0.419377 | − | 0.907812i | \(-0.362249\pi\) | ||||
0.419377 | + | 0.907812i | \(0.362249\pi\) | |||||||
\(38\) | −7.50326e6 | −0.583745 | ||||||||
\(39\) | 1.09659e6 | 0.0759022 | ||||||||
\(40\) | −3.33049e6 | −0.205702 | ||||||||
\(41\) | 2.55441e7 | 1.41177 | 0.705884 | − | 0.708327i | \(-0.250550\pi\) | ||||
0.705884 | + | 0.708327i | \(0.250550\pi\) | |||||||
\(42\) | −2.28046e6 | −0.113084 | ||||||||
\(43\) | 2.04501e7 | 0.912196 | 0.456098 | − | 0.889929i | \(-0.349247\pi\) | ||||
0.456098 | + | 0.889929i | \(0.349247\pi\) | |||||||
\(44\) | −8.91872e6 | −0.358728 | ||||||||
\(45\) | 4.40195e6 | 0.160025 | ||||||||
\(46\) | −4.98310e7 | −1.64093 | ||||||||
\(47\) | 2.39334e7 | 0.715424 | 0.357712 | − | 0.933832i | \(-0.383557\pi\) | ||||
0.357712 | + | 0.933832i | \(0.383557\pi\) | |||||||
\(48\) | −2.62170e7 | −0.712848 | ||||||||
\(49\) | −3.92076e7 | −0.971602 | ||||||||
\(50\) | 4.66158e7 | 1.05480 | ||||||||
\(51\) | −3.15484e7 | −0.652998 | ||||||||
\(52\) | 1.76996e6 | 0.0335697 | ||||||||
\(53\) | −8.96199e7 | −1.56014 | −0.780069 | − | 0.625694i | \(-0.784816\pi\) | ||||
−0.780069 | + | 0.625694i | \(0.784816\pi\) | |||||||
\(54\) | 6.89223e7 | 1.10303 | ||||||||
\(55\) | 2.29245e7 | 0.337806 | ||||||||
\(56\) | 1.02624e7 | 0.139445 | ||||||||
\(57\) | 2.46987e7 | 0.309911 | ||||||||
\(58\) | 1.64185e8 | 1.90505 | ||||||||
\(59\) | −1.28977e8 | −1.38572 | −0.692862 | − | 0.721070i | \(-0.743650\pi\) | ||||
−0.692862 | + | 0.721070i | \(0.743650\pi\) | |||||||
\(60\) | −3.93208e6 | −0.0391689 | ||||||||
\(61\) | 1.09979e8 | 1.01701 | 0.508504 | − | 0.861059i | \(-0.330199\pi\) | ||||
0.508504 | + | 0.861059i | \(0.330199\pi\) | |||||||
\(62\) | 6.30965e7 | 0.542304 | ||||||||
\(63\) | −1.35640e7 | −0.108481 | ||||||||
\(64\) | 8.25489e7 | 0.615037 | ||||||||
\(65\) | −4.54946e6 | −0.0316118 | ||||||||
\(66\) | 1.40570e8 | 0.911892 | ||||||||
\(67\) | −2.48183e8 | −1.50465 | −0.752324 | − | 0.658793i | \(-0.771067\pi\) | ||||
−0.752324 | + | 0.658793i | \(0.771067\pi\) | |||||||
\(68\) | −5.09208e7 | −0.288805 | ||||||||
\(69\) | 1.64030e8 | 0.871170 | ||||||||
\(70\) | 9.46099e6 | 0.0470972 | ||||||||
\(71\) | −3.36200e8 | −1.57013 | −0.785064 | − | 0.619414i | \(-0.787370\pi\) | ||||
−0.785064 | + | 0.619414i | \(0.787370\pi\) | |||||||
\(72\) | −1.21469e8 | −0.532681 | ||||||||
\(73\) | −7.56846e7 | −0.311928 | −0.155964 | − | 0.987763i | \(-0.549848\pi\) | ||||
−0.155964 | + | 0.987763i | \(0.549848\pi\) | |||||||
\(74\) | −2.43247e8 | −0.942986 | ||||||||
\(75\) | −1.53447e8 | −0.559992 | ||||||||
\(76\) | 3.98650e7 | 0.137066 | ||||||||
\(77\) | −7.06385e7 | −0.228999 | ||||||||
\(78\) | −2.78966e7 | −0.0853346 | ||||||||
\(79\) | 4.76941e7 | 0.137766 | 0.0688831 | − | 0.997625i | \(-0.478056\pi\) | ||||
0.0688831 | + | 0.997625i | \(0.478056\pi\) | |||||||
\(80\) | 1.08767e8 | 0.296887 | ||||||||
\(81\) | 2.25237e7 | 0.0581375 | ||||||||
\(82\) | −6.49825e8 | −1.58721 | ||||||||
\(83\) | 1.87443e8 | 0.433528 | 0.216764 | − | 0.976224i | \(-0.430450\pi\) | ||||
0.216764 | + | 0.976224i | \(0.430450\pi\) | |||||||
\(84\) | 1.21161e7 | 0.0265526 | ||||||||
\(85\) | 1.30886e8 | 0.271961 | ||||||||
\(86\) | −5.20238e8 | −1.02556 | ||||||||
\(87\) | −5.40452e8 | −1.01140 | ||||||||
\(88\) | −6.32584e8 | −1.12447 | ||||||||
\(89\) | 3.24624e8 | 0.548436 | 0.274218 | − | 0.961668i | \(-0.411581\pi\) | ||||
0.274218 | + | 0.961668i | \(0.411581\pi\) | |||||||
\(90\) | −1.11983e8 | −0.179912 | ||||||||
\(91\) | 1.40185e7 | 0.0214296 | ||||||||
\(92\) | 2.64753e8 | 0.385297 | ||||||||
\(93\) | −2.07697e8 | −0.287910 | ||||||||
\(94\) | −6.08849e8 | −0.804330 | ||||||||
\(95\) | −1.02468e8 | −0.129072 | ||||||||
\(96\) | 2.55922e8 | 0.307529 | ||||||||
\(97\) | 3.89600e7 | 0.0446834 | 0.0223417 | − | 0.999750i | \(-0.492888\pi\) | ||||
0.0223417 | + | 0.999750i | \(0.492888\pi\) | |||||||
\(98\) | 9.97416e8 | 1.09234 | ||||||||
\(99\) | 8.36095e8 | 0.874777 | ||||||||
\(100\) | −2.47671e8 | −0.247671 | ||||||||
\(101\) | −1.12674e9 | −1.07740 | −0.538700 | − | 0.842498i | \(-0.681084\pi\) | ||||
−0.538700 | + | 0.842498i | \(0.681084\pi\) | |||||||
\(102\) | 8.02571e8 | 0.734147 | ||||||||
\(103\) | −8.18572e8 | −0.716621 | −0.358310 | − | 0.933603i | \(-0.616647\pi\) | ||||
−0.358310 | + | 0.933603i | \(0.616647\pi\) | |||||||
\(104\) | 1.25539e8 | 0.105227 | ||||||||
\(105\) | −3.11430e7 | −0.0250040 | ||||||||
\(106\) | 2.27987e9 | 1.75402 | ||||||||
\(107\) | 1.13627e8 | 0.0838023 | 0.0419012 | − | 0.999122i | \(-0.486659\pi\) | ||||
0.0419012 | + | 0.999122i | \(0.486659\pi\) | |||||||
\(108\) | −3.66186e8 | −0.258997 | ||||||||
\(109\) | 2.43020e9 | 1.64901 | 0.824506 | − | 0.565854i | \(-0.191453\pi\) | ||||
0.824506 | + | 0.565854i | \(0.191453\pi\) | |||||||
\(110\) | −5.83184e8 | −0.379786 | ||||||||
\(111\) | 8.00705e8 | 0.500632 | ||||||||
\(112\) | −3.35149e8 | −0.201260 | ||||||||
\(113\) | 8.33615e8 | 0.480964 | 0.240482 | − | 0.970654i | \(-0.422694\pi\) | ||||
0.240482 | + | 0.970654i | \(0.422694\pi\) | |||||||
\(114\) | −6.28319e8 | −0.348424 | ||||||||
\(115\) | −6.80516e8 | −0.362826 | ||||||||
\(116\) | −8.72318e8 | −0.447315 | ||||||||
\(117\) | −1.65926e8 | −0.0818614 | ||||||||
\(118\) | 3.28108e9 | 1.55793 | ||||||||
\(119\) | −4.03305e8 | −0.184362 | ||||||||
\(120\) | −2.78893e8 | −0.122779 | ||||||||
\(121\) | 1.99627e9 | 0.846614 | ||||||||
\(122\) | −2.79779e9 | −1.14339 | ||||||||
\(123\) | 2.13905e9 | 0.842651 | ||||||||
\(124\) | −3.35233e8 | −0.127335 | ||||||||
\(125\) | 1.31515e9 | 0.481814 | ||||||||
\(126\) | 3.45058e8 | 0.121962 | ||||||||
\(127\) | 1.98972e9 | 0.678695 | 0.339348 | − | 0.940661i | \(-0.389794\pi\) | ||||
0.339348 | + | 0.940661i | \(0.389794\pi\) | |||||||
\(128\) | −3.66475e9 | −1.20670 | ||||||||
\(129\) | 1.71248e9 | 0.544469 | ||||||||
\(130\) | 1.15735e8 | 0.0355402 | ||||||||
\(131\) | 1.15149e9 | 0.341618 | 0.170809 | − | 0.985304i | \(-0.445362\pi\) | ||||
0.170809 | + | 0.985304i | \(0.445362\pi\) | |||||||
\(132\) | −7.46849e8 | −0.214117 | ||||||||
\(133\) | 3.15740e8 | 0.0874979 | ||||||||
\(134\) | 6.31360e9 | 1.69163 | ||||||||
\(135\) | 9.41237e8 | 0.243892 | ||||||||
\(136\) | −3.61169e9 | −0.905285 | ||||||||
\(137\) | 3.87948e9 | 0.940873 | 0.470437 | − | 0.882434i | \(-0.344096\pi\) | ||||
0.470437 | + | 0.882434i | \(0.344096\pi\) | |||||||
\(138\) | −4.17282e9 | −0.979431 | ||||||||
\(139\) | 1.00219e9 | 0.227712 | 0.113856 | − | 0.993497i | \(-0.463680\pi\) | ||||
0.113856 | + | 0.993497i | \(0.463680\pi\) | |||||||
\(140\) | −5.02665e7 | −0.0110587 | ||||||||
\(141\) | 2.00417e9 | 0.427020 | ||||||||
\(142\) | 8.55271e9 | 1.76525 | ||||||||
\(143\) | −8.64112e8 | −0.172806 | ||||||||
\(144\) | 3.96691e9 | 0.768814 | ||||||||
\(145\) | 2.24219e9 | 0.421227 | ||||||||
\(146\) | 1.92537e9 | 0.350692 | ||||||||
\(147\) | −3.28323e9 | −0.579926 | ||||||||
\(148\) | 1.29238e9 | 0.221418 | ||||||||
\(149\) | 2.90922e9 | 0.483546 | 0.241773 | − | 0.970333i | \(-0.422271\pi\) | ||||
0.241773 | + | 0.970333i | \(0.422271\pi\) | |||||||
\(150\) | 3.90358e9 | 0.629582 | ||||||||
\(151\) | 8.62779e9 | 1.35053 | 0.675264 | − | 0.737576i | \(-0.264030\pi\) | ||||
0.675264 | + | 0.737576i | \(0.264030\pi\) | |||||||
\(152\) | 2.82753e9 | 0.429646 | ||||||||
\(153\) | 4.77363e9 | 0.704266 | ||||||||
\(154\) | 1.79700e9 | 0.257456 | ||||||||
\(155\) | 8.61676e8 | 0.119909 | ||||||||
\(156\) | 1.48215e8 | 0.0200370 | ||||||||
\(157\) | 1.03295e10 | 1.35685 | 0.678426 | − | 0.734669i | \(-0.262662\pi\) | ||||
0.678426 | + | 0.734669i | \(0.262662\pi\) | |||||||
\(158\) | −1.21331e9 | −0.154887 | ||||||||
\(159\) | −7.50472e9 | −0.931210 | ||||||||
\(160\) | −1.06175e9 | −0.128080 | ||||||||
\(161\) | 2.09691e9 | 0.245959 | ||||||||
\(162\) | −5.72987e8 | −0.0653623 | ||||||||
\(163\) | −8.87803e9 | −0.985083 | −0.492541 | − | 0.870289i | \(-0.663932\pi\) | ||||
−0.492541 | + | 0.870289i | \(0.663932\pi\) | |||||||
\(164\) | 3.45254e9 | 0.372684 | ||||||||
\(165\) | 1.91969e9 | 0.201629 | ||||||||
\(166\) | −4.76842e9 | −0.487402 | ||||||||
\(167\) | 1.35813e10 | 1.35120 | 0.675598 | − | 0.737270i | \(-0.263885\pi\) | ||||
0.675598 | + | 0.737270i | \(0.263885\pi\) | |||||||
\(168\) | 8.59368e8 | 0.0832314 | ||||||||
\(169\) | −1.04330e10 | −0.983829 | ||||||||
\(170\) | −3.32965e9 | −0.305758 | ||||||||
\(171\) | −3.73719e9 | −0.334243 | ||||||||
\(172\) | 2.76404e9 | 0.240805 | ||||||||
\(173\) | 1.38587e10 | 1.17629 | 0.588145 | − | 0.808755i | \(-0.299858\pi\) | ||||
0.588145 | + | 0.808755i | \(0.299858\pi\) | |||||||
\(174\) | 1.37488e10 | 1.13708 | ||||||||
\(175\) | −1.96161e9 | −0.158104 | ||||||||
\(176\) | 2.06589e10 | 1.62293 | ||||||||
\(177\) | −1.08004e10 | −0.827106 | ||||||||
\(178\) | −8.25823e9 | −0.616591 | ||||||||
\(179\) | 6.49482e9 | 0.472855 | 0.236428 | − | 0.971649i | \(-0.424023\pi\) | ||||
0.236428 | + | 0.971649i | \(0.424023\pi\) | |||||||
\(180\) | 5.94967e8 | 0.0422442 | ||||||||
\(181\) | 9.54862e9 | 0.661282 | 0.330641 | − | 0.943757i | \(-0.392735\pi\) | ||||
0.330641 | + | 0.943757i | \(0.392735\pi\) | |||||||
\(182\) | −3.56621e8 | −0.0240927 | ||||||||
\(183\) | 9.20956e9 | 0.607029 | ||||||||
\(184\) | 1.87783e10 | 1.20775 | ||||||||
\(185\) | −3.32190e9 | −0.208504 | ||||||||
\(186\) | 5.28366e9 | 0.323688 | ||||||||
\(187\) | 2.48601e10 | 1.48667 | ||||||||
\(188\) | 3.23483e9 | 0.188861 | ||||||||
\(189\) | −2.90028e9 | −0.165334 | ||||||||
\(190\) | 2.60672e9 | 0.145112 | ||||||||
\(191\) | 1.84838e10 | 1.00494 | 0.502470 | − | 0.864594i | \(-0.332425\pi\) | ||||
0.502470 | + | 0.864594i | \(0.332425\pi\) | |||||||
\(192\) | 6.91260e9 | 0.367101 | ||||||||
\(193\) | −2.87866e10 | −1.49342 | −0.746711 | − | 0.665149i | \(-0.768368\pi\) | ||||
−0.746711 | + | 0.665149i | \(0.768368\pi\) | |||||||
\(194\) | −9.91116e8 | −0.0502362 | ||||||||
\(195\) | −3.80969e8 | −0.0188684 | ||||||||
\(196\) | −5.29930e9 | −0.256487 | ||||||||
\(197\) | 1.50614e9 | 0.0712470 | ||||||||
\(198\) | −2.12697e10 | −0.983486 | ||||||||
\(199\) | 2.01842e10 | 0.912374 | 0.456187 | − | 0.889884i | \(-0.349215\pi\) | ||||
0.456187 | + | 0.889884i | \(0.349215\pi\) | |||||||
\(200\) | −1.75667e10 | −0.776346 | ||||||||
\(201\) | −2.07827e10 | −0.898089 | ||||||||
\(202\) | 2.86635e10 | 1.21129 | ||||||||
\(203\) | −6.90897e9 | −0.285549 | ||||||||
\(204\) | −4.26408e9 | −0.172381 | ||||||||
\(205\) | −8.87433e9 | −0.350948 | ||||||||
\(206\) | 2.08239e10 | 0.805675 | ||||||||
\(207\) | −2.48196e10 | −0.939567 | ||||||||
\(208\) | −4.09984e9 | −0.151873 | ||||||||
\(209\) | −1.94625e10 | −0.705571 | ||||||||
\(210\) | 7.92258e8 | 0.0281112 | ||||||||
\(211\) | 5.18101e10 | 1.79947 | 0.899733 | − | 0.436441i | \(-0.143761\pi\) | ||||
0.899733 | + | 0.436441i | \(0.143761\pi\) | |||||||
\(212\) | −1.21130e10 | −0.411851 | ||||||||
\(213\) | −2.81532e10 | −0.937173 | ||||||||
\(214\) | −2.89061e9 | −0.0942165 | ||||||||
\(215\) | −7.10462e9 | −0.226761 | ||||||||
\(216\) | −2.59727e10 | −0.811849 | ||||||||
\(217\) | −2.65513e9 | −0.0812861 | ||||||||
\(218\) | −6.18228e10 | −1.85393 | ||||||||
\(219\) | −6.33779e9 | −0.186183 | ||||||||
\(220\) | 3.09847e9 | 0.0891755 | ||||||||
\(221\) | −4.93358e9 | −0.139122 | ||||||||
\(222\) | −2.03694e10 | −0.562846 | ||||||||
\(223\) | −5.04084e9 | −0.136499 | −0.0682497 | − | 0.997668i | \(-0.521741\pi\) | ||||
−0.0682497 | + | 0.997668i | \(0.521741\pi\) | |||||||
\(224\) | 3.27162e9 | 0.0868254 | ||||||||
\(225\) | 2.32182e10 | 0.603958 | ||||||||
\(226\) | −2.12066e10 | −0.540734 | ||||||||
\(227\) | −7.67396e9 | −0.191824 | −0.0959121 | − | 0.995390i | \(-0.530577\pi\) | ||||
−0.0959121 | + | 0.995390i | \(0.530577\pi\) | |||||||
\(228\) | 3.33827e9 | 0.0818116 | ||||||||
\(229\) | 3.85554e10 | 0.926457 | 0.463229 | − | 0.886239i | \(-0.346691\pi\) | ||||
0.463229 | + | 0.886239i | \(0.346691\pi\) | |||||||
\(230\) | 1.73119e10 | 0.407914 | ||||||||
\(231\) | −5.91523e9 | −0.136684 | ||||||||
\(232\) | −6.18715e10 | −1.40215 | ||||||||
\(233\) | 3.08810e10 | 0.686419 | 0.343210 | − | 0.939259i | \(-0.388486\pi\) | ||||
0.343210 | + | 0.939259i | \(0.388486\pi\) | |||||||
\(234\) | 4.22106e9 | 0.0920343 | ||||||||
\(235\) | −8.31474e9 | −0.177846 | ||||||||
\(236\) | −1.74324e10 | −0.365809 | ||||||||
\(237\) | 3.99388e9 | 0.0822294 | ||||||||
\(238\) | 1.02598e10 | 0.207273 | ||||||||
\(239\) | 6.43440e10 | 1.27561 | 0.637804 | − | 0.770199i | \(-0.279843\pi\) | ||||
0.637804 | + | 0.770199i | \(0.279843\pi\) | |||||||
\(240\) | 9.10808e9 | 0.177205 | ||||||||
\(241\) | −5.98359e10 | −1.14258 | −0.571289 | − | 0.820749i | \(-0.693556\pi\) | ||||
−0.571289 | + | 0.820749i | \(0.693556\pi\) | |||||||
\(242\) | −5.07838e10 | −0.951823 | ||||||||
\(243\) | 5.52129e10 | 1.01581 | ||||||||
\(244\) | 1.48647e10 | 0.268474 | ||||||||
\(245\) | 1.36212e10 | 0.241528 | ||||||||
\(246\) | −5.44160e10 | −0.947368 | ||||||||
\(247\) | 3.86241e9 | 0.0660271 | ||||||||
\(248\) | −2.37773e10 | −0.399144 | ||||||||
\(249\) | 1.56963e10 | 0.258763 | ||||||||
\(250\) | −3.34565e10 | −0.541689 | ||||||||
\(251\) | −5.21882e10 | −0.829928 | −0.414964 | − | 0.909838i | \(-0.636206\pi\) | ||||
−0.414964 | + | 0.909838i | \(0.636206\pi\) | |||||||
\(252\) | −1.83330e9 | −0.0286373 | ||||||||
\(253\) | −1.29255e11 | −1.98338 | ||||||||
\(254\) | −5.06171e10 | −0.763037 | ||||||||
\(255\) | 1.09603e10 | 0.162327 | ||||||||
\(256\) | 5.09637e10 | 0.741619 | ||||||||
\(257\) | 3.63401e9 | 0.0519622 | 0.0259811 | − | 0.999662i | \(-0.491729\pi\) | ||||
0.0259811 | + | 0.999662i | \(0.491729\pi\) | |||||||
\(258\) | −4.35645e10 | −0.612130 | ||||||||
\(259\) | 1.02360e10 | 0.141345 | ||||||||
\(260\) | −6.14904e8 | −0.00834501 | ||||||||
\(261\) | 8.17764e10 | 1.09080 | ||||||||
\(262\) | −2.92932e10 | −0.384071 | ||||||||
\(263\) | −1.05265e11 | −1.35669 | −0.678347 | − | 0.734742i | \(-0.737303\pi\) | ||||
−0.678347 | + | 0.734742i | \(0.737303\pi\) | |||||||
\(264\) | −5.29722e10 | −0.671167 | ||||||||
\(265\) | 3.11350e10 | 0.387831 | ||||||||
\(266\) | −8.03222e9 | −0.0983713 | ||||||||
\(267\) | 2.71839e10 | 0.327349 | ||||||||
\(268\) | −3.35443e10 | −0.397203 | ||||||||
\(269\) | 1.45429e11 | 1.69343 | 0.846713 | − | 0.532050i | \(-0.178578\pi\) | ||||
0.846713 | + | 0.532050i | \(0.178578\pi\) | |||||||
\(270\) | −2.39444e10 | −0.274200 | ||||||||
\(271\) | −8.79643e10 | −0.990706 | −0.495353 | − | 0.868692i | \(-0.664961\pi\) | ||||
−0.495353 | + | 0.868692i | \(0.664961\pi\) | |||||||
\(272\) | 1.17950e11 | 1.30659 | ||||||||
\(273\) | 1.17390e9 | 0.0127908 | ||||||||
\(274\) | −9.86915e10 | −1.05780 | ||||||||
\(275\) | 1.20916e11 | 1.27493 | ||||||||
\(276\) | 2.21703e10 | 0.229975 | ||||||||
\(277\) | 1.24181e11 | 1.26734 | 0.633672 | − | 0.773602i | \(-0.281547\pi\) | ||||
0.633672 | + | 0.773602i | \(0.281547\pi\) | |||||||
\(278\) | −2.54952e10 | −0.256010 | ||||||||
\(279\) | 3.14268e10 | 0.310514 | ||||||||
\(280\) | −3.56528e9 | −0.0346643 | ||||||||
\(281\) | −3.62284e10 | −0.346633 | −0.173317 | − | 0.984866i | \(-0.555448\pi\) | ||||
−0.173317 | + | 0.984866i | \(0.555448\pi\) | |||||||
\(282\) | −5.09847e10 | −0.480086 | ||||||||
\(283\) | −4.57153e10 | −0.423665 | −0.211833 | − | 0.977306i | \(-0.567943\pi\) | ||||
−0.211833 | + | 0.977306i | \(0.567943\pi\) | |||||||
\(284\) | −4.54407e10 | −0.414489 | ||||||||
\(285\) | −8.58062e9 | −0.0770401 | ||||||||
\(286\) | 2.19824e10 | 0.194280 | ||||||||
\(287\) | 2.73449e10 | 0.237908 | ||||||||
\(288\) | −3.87238e10 | −0.331674 | ||||||||
\(289\) | 2.33490e10 | 0.196892 | ||||||||
\(290\) | −5.70398e10 | −0.473573 | ||||||||
\(291\) | 3.26249e9 | 0.0266704 | ||||||||
\(292\) | −1.02295e10 | −0.0823441 | ||||||||
\(293\) | −8.36775e10 | −0.663292 | −0.331646 | − | 0.943404i | \(-0.607604\pi\) | ||||
−0.331646 | + | 0.943404i | \(0.607604\pi\) | |||||||
\(294\) | 8.35231e10 | 0.651994 | ||||||||
\(295\) | 4.48080e10 | 0.344474 | ||||||||
\(296\) | 9.16653e10 | 0.694053 | ||||||||
\(297\) | 1.78776e11 | 1.33323 | ||||||||
\(298\) | −7.40086e10 | −0.543637 | ||||||||
\(299\) | 2.56513e10 | 0.185604 | ||||||||
\(300\) | −2.07398e10 | −0.147829 | ||||||||
\(301\) | 2.18918e10 | 0.153721 | ||||||||
\(302\) | −2.19485e11 | −1.51836 | ||||||||
\(303\) | −9.43524e10 | −0.643074 | ||||||||
\(304\) | −9.23413e10 | −0.620105 | ||||||||
\(305\) | −3.82079e10 | −0.252816 | ||||||||
\(306\) | −1.21438e11 | −0.791786 | ||||||||
\(307\) | −1.54276e11 | −0.991235 | −0.495618 | − | 0.868541i | \(-0.665058\pi\) | ||||
−0.495618 | + | 0.868541i | \(0.665058\pi\) | |||||||
\(308\) | −9.54748e9 | −0.0604520 | ||||||||
\(309\) | −6.85468e10 | −0.427734 | ||||||||
\(310\) | −2.19205e10 | −0.134810 | ||||||||
\(311\) | −1.33921e11 | −0.811758 | −0.405879 | − | 0.913927i | \(-0.633034\pi\) | ||||
−0.405879 | + | 0.913927i | \(0.633034\pi\) | |||||||
\(312\) | 1.05125e10 | 0.0628076 | ||||||||
\(313\) | 2.35267e11 | 1.38551 | 0.692757 | − | 0.721171i | \(-0.256396\pi\) | ||||
0.692757 | + | 0.721171i | \(0.256396\pi\) | |||||||
\(314\) | −2.62777e11 | −1.52547 | ||||||||
\(315\) | 4.71228e9 | 0.0269671 | ||||||||
\(316\) | 6.44633e9 | 0.0363681 | ||||||||
\(317\) | −2.55517e11 | −1.42119 | −0.710597 | − | 0.703599i | \(-0.751575\pi\) | ||||
−0.710597 | + | 0.703599i | \(0.751575\pi\) | |||||||
\(318\) | 1.90915e11 | 1.04693 | ||||||||
\(319\) | 4.25875e11 | 2.30263 | ||||||||
\(320\) | −2.86785e10 | −0.152891 | ||||||||
\(321\) | 9.51510e9 | 0.0500197 | ||||||||
\(322\) | −5.33440e10 | −0.276525 | ||||||||
\(323\) | −1.11120e11 | −0.568042 | ||||||||
\(324\) | 3.04429e9 | 0.0153474 | ||||||||
\(325\) | −2.39962e10 | −0.119307 | ||||||||
\(326\) | 2.25851e11 | 1.10750 | ||||||||
\(327\) | 2.03504e11 | 0.984256 | ||||||||
\(328\) | 2.44880e11 | 1.16821 | ||||||||
\(329\) | 2.56206e10 | 0.120561 | ||||||||
\(330\) | −4.88355e10 | −0.226685 | ||||||||
\(331\) | −5.77463e10 | −0.264423 | −0.132211 | − | 0.991222i | \(-0.542208\pi\) | ||||
−0.132211 | + | 0.991222i | \(0.542208\pi\) | |||||||
\(332\) | 2.53347e10 | 0.114444 | ||||||||
\(333\) | −1.21155e11 | −0.539938 | ||||||||
\(334\) | −3.45500e11 | −1.51911 | ||||||||
\(335\) | 8.62216e10 | 0.374037 | ||||||||
\(336\) | −2.80652e10 | −0.120127 | ||||||||
\(337\) | 1.88165e11 | 0.794703 | 0.397351 | − | 0.917667i | \(-0.369929\pi\) | ||||
0.397351 | + | 0.917667i | \(0.369929\pi\) | |||||||
\(338\) | 2.65409e11 | 1.10609 | ||||||||
\(339\) | 6.98065e10 | 0.287076 | ||||||||
\(340\) | 1.76905e10 | 0.0717935 | ||||||||
\(341\) | 1.63664e11 | 0.655480 | ||||||||
\(342\) | 9.50715e10 | 0.375779 | ||||||||
\(343\) | −8.51702e10 | −0.332249 | ||||||||
\(344\) | 1.96047e11 | 0.754825 | ||||||||
\(345\) | −5.69861e10 | −0.216562 | ||||||||
\(346\) | −3.52556e11 | −1.32247 | ||||||||
\(347\) | −8.77882e10 | −0.325052 | −0.162526 | − | 0.986704i | \(-0.551964\pi\) | ||||
−0.162526 | + | 0.986704i | \(0.551964\pi\) | |||||||
\(348\) | −7.30474e10 | −0.266992 | ||||||||
\(349\) | 4.79459e11 | 1.72996 | 0.864982 | − | 0.501803i | \(-0.167330\pi\) | ||||
0.864982 | + | 0.501803i | \(0.167330\pi\) | |||||||
\(350\) | 4.99021e10 | 0.177751 | ||||||||
\(351\) | −3.54788e10 | −0.124763 | ||||||||
\(352\) | −2.01666e11 | −0.700149 | ||||||||
\(353\) | −5.95046e10 | −0.203969 | −0.101985 | − | 0.994786i | \(-0.532519\pi\) | ||||
−0.101985 | + | 0.994786i | \(0.532519\pi\) | |||||||
\(354\) | 2.74756e11 | 0.929891 | ||||||||
\(355\) | 1.16800e11 | 0.390315 | ||||||||
\(356\) | 4.38762e10 | 0.144778 | ||||||||
\(357\) | −3.37725e10 | −0.110042 | ||||||||
\(358\) | −1.65224e11 | −0.531617 | ||||||||
\(359\) | 6.61235e10 | 0.210102 | 0.105051 | − | 0.994467i | \(-0.466499\pi\) | ||||
0.105051 | + | 0.994467i | \(0.466499\pi\) | |||||||
\(360\) | 4.21996e10 | 0.132418 | ||||||||
\(361\) | −2.35694e11 | −0.730409 | ||||||||
\(362\) | −2.42910e11 | −0.743460 | ||||||||
\(363\) | 1.67167e11 | 0.505324 | ||||||||
\(364\) | 1.89473e9 | 0.00565708 | ||||||||
\(365\) | 2.62937e10 | 0.0775416 | ||||||||
\(366\) | −2.34285e11 | −0.682464 | ||||||||
\(367\) | 4.31936e11 | 1.24286 | 0.621430 | − | 0.783470i | \(-0.286552\pi\) | ||||
0.621430 | + | 0.783470i | \(0.286552\pi\) | |||||||
\(368\) | −6.13262e11 | −1.74313 | ||||||||
\(369\) | −3.23662e11 | −0.908809 | ||||||||
\(370\) | 8.45070e10 | 0.234415 | ||||||||
\(371\) | −9.59380e10 | −0.262910 | ||||||||
\(372\) | −2.80722e10 | −0.0760035 | ||||||||
\(373\) | 2.34458e11 | 0.627155 | 0.313578 | − | 0.949563i | \(-0.398472\pi\) | ||||
0.313578 | + | 0.949563i | \(0.398472\pi\) | |||||||
\(374\) | −6.32424e11 | −1.67142 | ||||||||
\(375\) | 1.10130e11 | 0.287583 | ||||||||
\(376\) | 2.29439e11 | 0.592000 | ||||||||
\(377\) | −8.45166e10 | −0.215480 | ||||||||
\(378\) | 7.37812e10 | 0.185880 | ||||||||
\(379\) | 1.71270e11 | 0.426388 | 0.213194 | − | 0.977010i | \(-0.431613\pi\) | ||||
0.213194 | + | 0.977010i | \(0.431613\pi\) | |||||||
\(380\) | −1.38496e10 | −0.0340730 | ||||||||
\(381\) | 1.66618e11 | 0.405097 | ||||||||
\(382\) | −4.70215e11 | −1.12982 | ||||||||
\(383\) | −5.78488e11 | −1.37373 | −0.686863 | − | 0.726787i | \(-0.741013\pi\) | ||||
−0.686863 | + | 0.726787i | \(0.741013\pi\) | |||||||
\(384\) | −3.06884e11 | −0.720251 | ||||||||
\(385\) | 2.45406e10 | 0.0569263 | ||||||||
\(386\) | 7.32312e11 | 1.67901 | ||||||||
\(387\) | −2.59118e11 | −0.587216 | ||||||||
\(388\) | 5.26582e9 | 0.0117957 | ||||||||
\(389\) | 1.87685e11 | 0.415581 | 0.207791 | − | 0.978173i | \(-0.433373\pi\) | ||||
0.207791 | + | 0.978173i | \(0.433373\pi\) | |||||||
\(390\) | 9.69160e9 | 0.0212131 | ||||||||
\(391\) | −7.37975e11 | −1.59678 | ||||||||
\(392\) | −3.75867e11 | −0.803982 | ||||||||
\(393\) | 9.64254e10 | 0.203904 | ||||||||
\(394\) | −3.83152e10 | −0.0801010 | ||||||||
\(395\) | −1.65695e10 | −0.0342470 | ||||||||
\(396\) | 1.13006e11 | 0.230927 | ||||||||
\(397\) | −6.80816e10 | −0.137554 | −0.0687769 | − | 0.997632i | \(-0.521910\pi\) | ||||
−0.0687769 | + | 0.997632i | \(0.521910\pi\) | |||||||
\(398\) | −5.13473e11 | −1.02575 | ||||||||
\(399\) | 2.64399e10 | 0.0522254 | ||||||||
\(400\) | 5.73693e11 | 1.12049 | ||||||||
\(401\) | −3.21067e11 | −0.620077 | −0.310039 | − | 0.950724i | \(-0.600342\pi\) | ||||
−0.310039 | + | 0.950724i | \(0.600342\pi\) | |||||||
\(402\) | 5.28698e11 | 1.00969 | ||||||||
\(403\) | −3.24799e10 | −0.0613397 | ||||||||
\(404\) | −1.52290e11 | −0.284416 | ||||||||
\(405\) | −7.82499e9 | −0.0144523 | ||||||||
\(406\) | 1.75760e11 | 0.321035 | ||||||||
\(407\) | −6.30954e11 | −1.13978 | ||||||||
\(408\) | −3.02441e11 | −0.540344 | ||||||||
\(409\) | 1.03455e12 | 1.82808 | 0.914042 | − | 0.405619i | \(-0.132944\pi\) | ||||
0.914042 | + | 0.405619i | \(0.132944\pi\) | |||||||
\(410\) | 2.25757e11 | 0.394561 | ||||||||
\(411\) | 3.24866e11 | 0.561585 | ||||||||
\(412\) | −1.10638e11 | −0.189176 | ||||||||
\(413\) | −1.38069e11 | −0.233519 | ||||||||
\(414\) | 6.31394e11 | 1.05633 | ||||||||
\(415\) | −6.51198e10 | −0.107770 | ||||||||
\(416\) | 4.00214e10 | 0.0655197 | ||||||||
\(417\) | 8.39232e10 | 0.135916 | ||||||||
\(418\) | 4.95114e11 | 0.793253 | ||||||||
\(419\) | −8.26593e11 | −1.31017 | −0.655087 | − | 0.755554i | \(-0.727368\pi\) | ||||
−0.655087 | + | 0.755554i | \(0.727368\pi\) | |||||||
\(420\) | −4.20929e9 | −0.00660065 | ||||||||
\(421\) | 7.04223e11 | 1.09255 | 0.546274 | − | 0.837606i | \(-0.316046\pi\) | ||||
0.546274 | + | 0.837606i | \(0.316046\pi\) | |||||||
\(422\) | −1.31801e12 | −2.02309 | ||||||||
\(423\) | −3.03253e11 | −0.460546 | ||||||||
\(424\) | −8.59147e11 | −1.29098 | ||||||||
\(425\) | 6.90359e11 | 1.02642 | ||||||||
\(426\) | 7.16199e11 | 1.05364 | ||||||||
\(427\) | 1.17732e11 | 0.171384 | ||||||||
\(428\) | 1.53579e10 | 0.0221225 | ||||||||
\(429\) | −7.23603e10 | −0.103144 | ||||||||
\(430\) | 1.80737e11 | 0.254940 | ||||||||
\(431\) | 2.75449e11 | 0.384498 | 0.192249 | − | 0.981346i | \(-0.438422\pi\) | ||||
0.192249 | + | 0.981346i | \(0.438422\pi\) | |||||||
\(432\) | 8.48216e11 | 1.17173 | ||||||||
\(433\) | 1.00904e9 | 0.00137947 | 0.000689734 | − | 1.00000i | \(-0.499780\pi\) | ||||
0.000689734 | 1.00000i | \(0.499780\pi\) | ||||||||
\(434\) | 6.75447e10 | 0.0913876 | ||||||||
\(435\) | 1.87760e11 | 0.251420 | ||||||||
\(436\) | 3.28466e11 | 0.435313 | ||||||||
\(437\) | 5.77747e11 | 0.757829 | ||||||||
\(438\) | 1.61229e11 | 0.209320 | ||||||||
\(439\) | 8.24219e11 | 1.05914 | 0.529569 | − | 0.848267i | \(-0.322354\pi\) | ||||
0.529569 | + | 0.848267i | \(0.322354\pi\) | |||||||
\(440\) | 2.19767e11 | 0.279528 | ||||||||
\(441\) | 4.96788e11 | 0.625457 | ||||||||
\(442\) | 1.25507e11 | 0.156411 | ||||||||
\(443\) | −1.44616e12 | −1.78402 | −0.892010 | − | 0.452015i | \(-0.850705\pi\) | ||||
−0.892010 | + | 0.452015i | \(0.850705\pi\) | |||||||
\(444\) | 1.08223e11 | 0.132159 | ||||||||
\(445\) | −1.12778e11 | −0.136335 | ||||||||
\(446\) | 1.28236e11 | 0.153462 | ||||||||
\(447\) | 2.43616e11 | 0.288617 | ||||||||
\(448\) | 8.83685e10 | 0.103645 | ||||||||
\(449\) | −2.16663e11 | −0.251580 | −0.125790 | − | 0.992057i | \(-0.540146\pi\) | ||||
−0.125790 | + | 0.992057i | \(0.540146\pi\) | |||||||
\(450\) | −5.90655e11 | −0.679012 | ||||||||
\(451\) | −1.68557e12 | −1.91845 | ||||||||
\(452\) | 1.12671e11 | 0.126967 | ||||||||
\(453\) | 7.22487e11 | 0.806098 | ||||||||
\(454\) | 1.95220e11 | 0.215662 | ||||||||
\(455\) | −4.87019e9 | −0.00532714 | ||||||||
\(456\) | 2.36776e11 | 0.256446 | ||||||||
\(457\) | −7.21024e11 | −0.773262 | −0.386631 | − | 0.922234i | \(-0.626361\pi\) | ||||
−0.386631 | + | 0.922234i | \(0.626361\pi\) | |||||||
\(458\) | −9.80823e11 | −1.04159 | ||||||||
\(459\) | 1.02071e12 | 1.07336 | ||||||||
\(460\) | −9.19785e10 | −0.0957802 | ||||||||
\(461\) | −1.95490e11 | −0.201591 | −0.100796 | − | 0.994907i | \(-0.532139\pi\) | ||||
−0.100796 | + | 0.994907i | \(0.532139\pi\) | |||||||
\(462\) | 1.50479e11 | 0.153670 | ||||||||
\(463\) | 1.48300e12 | 1.49978 | 0.749888 | − | 0.661564i | \(-0.230107\pi\) | ||||
0.749888 | + | 0.661564i | \(0.230107\pi\) | |||||||
\(464\) | 2.02060e12 | 2.02371 | ||||||||
\(465\) | 7.21563e10 | 0.0715708 | ||||||||
\(466\) | −7.85592e11 | −0.771721 | ||||||||
\(467\) | −1.15178e12 | −1.12058 | −0.560292 | − | 0.828295i | \(-0.689311\pi\) | ||||
−0.560292 | + | 0.828295i | \(0.689311\pi\) | |||||||
\(468\) | −2.24266e10 | −0.0216101 | ||||||||
\(469\) | −2.65679e11 | −0.253559 | ||||||||
\(470\) | 2.11521e11 | 0.199947 | ||||||||
\(471\) | 8.64990e11 | 0.809873 | ||||||||
\(472\) | −1.23644e12 | −1.14666 | ||||||||
\(473\) | −1.34943e12 | −1.23959 | ||||||||
\(474\) | −1.01602e11 | −0.0924481 | ||||||||
\(475\) | −5.40470e11 | −0.487136 | ||||||||
\(476\) | −5.45106e10 | −0.0486687 | ||||||||
\(477\) | 1.13555e12 | 1.00432 | ||||||||
\(478\) | −1.63687e12 | −1.43413 | ||||||||
\(479\) | 1.26546e12 | 1.09835 | 0.549174 | − | 0.835708i | \(-0.314942\pi\) | ||||
0.549174 | + | 0.835708i | \(0.314942\pi\) | |||||||
\(480\) | −8.89103e10 | −0.0764480 | ||||||||
\(481\) | 1.25215e11 | 0.106661 | ||||||||
\(482\) | 1.52219e12 | 1.28457 | ||||||||
\(483\) | 1.75594e11 | 0.146807 | ||||||||
\(484\) | 2.69816e11 | 0.223493 | ||||||||
\(485\) | −1.35352e10 | −0.0111077 | ||||||||
\(486\) | −1.40458e12 | −1.14204 | ||||||||
\(487\) | 1.09759e11 | 0.0884217 | 0.0442108 | − | 0.999022i | \(-0.485923\pi\) | ||||
0.0442108 | + | 0.999022i | \(0.485923\pi\) | |||||||
\(488\) | 1.05432e12 | 0.841555 | ||||||||
\(489\) | −7.43442e11 | −0.587973 | ||||||||
\(490\) | −3.46514e11 | −0.271543 | ||||||||
\(491\) | 2.19958e12 | 1.70794 | 0.853972 | − | 0.520319i | \(-0.174187\pi\) | ||||
0.853972 | + | 0.520319i | \(0.174187\pi\) | |||||||
\(492\) | 2.89114e11 | 0.222446 | ||||||||
\(493\) | 2.43150e12 | 1.85380 | ||||||||
\(494\) | −9.82572e10 | −0.0742324 | ||||||||
\(495\) | −2.90470e11 | −0.217459 | ||||||||
\(496\) | 7.76518e11 | 0.576081 | ||||||||
\(497\) | −3.59902e11 | −0.264594 | ||||||||
\(498\) | −3.99305e11 | −0.290919 | ||||||||
\(499\) | −2.49269e12 | −1.79977 | −0.899884 | − | 0.436130i | \(-0.856349\pi\) | ||||
−0.899884 | + | 0.436130i | \(0.856349\pi\) | |||||||
\(500\) | 1.77755e11 | 0.127191 | ||||||||
\(501\) | 1.13729e12 | 0.806498 | ||||||||
\(502\) | 1.32763e12 | 0.933063 | ||||||||
\(503\) | −7.65482e11 | −0.533186 | −0.266593 | − | 0.963809i | \(-0.585898\pi\) | ||||
−0.266593 | + | 0.963809i | \(0.585898\pi\) | |||||||
\(504\) | −1.30032e11 | −0.0897661 | ||||||||
\(505\) | 3.91442e11 | 0.267828 | ||||||||
\(506\) | 3.28817e12 | 2.22986 | ||||||||
\(507\) | −8.73655e11 | −0.587224 | ||||||||
\(508\) | 2.68930e11 | 0.179165 | ||||||||
\(509\) | 1.72021e12 | 1.13593 | 0.567966 | − | 0.823052i | \(-0.307731\pi\) | ||||
0.567966 | + | 0.823052i | \(0.307731\pi\) | |||||||
\(510\) | −2.78823e11 | −0.182500 | ||||||||
\(511\) | −8.10203e10 | −0.0525654 | ||||||||
\(512\) | 5.79868e11 | 0.372919 | ||||||||
\(513\) | −7.99094e11 | −0.509413 | ||||||||
\(514\) | −9.24469e10 | −0.0584196 | ||||||||
\(515\) | 2.84382e11 | 0.178143 | ||||||||
\(516\) | 2.31459e11 | 0.143731 | ||||||||
\(517\) | −1.57928e12 | −0.972191 | ||||||||
\(518\) | −2.60396e11 | −0.158910 | ||||||||
\(519\) | 1.16052e12 | 0.702100 | ||||||||
\(520\) | −4.36137e10 | −0.0261582 | ||||||||
\(521\) | −2.13972e12 | −1.27229 | −0.636147 | − | 0.771568i | \(-0.719473\pi\) | ||||
−0.636147 | + | 0.771568i | \(0.719473\pi\) | |||||||
\(522\) | −2.08034e12 | −1.22636 | ||||||||
\(523\) | 2.11674e12 | 1.23711 | 0.618557 | − | 0.785740i | \(-0.287717\pi\) | ||||
0.618557 | + | 0.785740i | \(0.287717\pi\) | |||||||
\(524\) | 1.55636e11 | 0.0901817 | ||||||||
\(525\) | −1.64264e11 | −0.0943684 | ||||||||
\(526\) | 2.67786e12 | 1.52529 | ||||||||
\(527\) | 9.34430e11 | 0.527715 | ||||||||
\(528\) | 1.72997e12 | 0.968690 | ||||||||
\(529\) | 2.03581e12 | 1.13028 | ||||||||
\(530\) | −7.92054e11 | −0.436027 | ||||||||
\(531\) | 1.63422e12 | 0.892044 | ||||||||
\(532\) | 4.26754e10 | 0.0230980 | ||||||||
\(533\) | 3.34507e11 | 0.179528 | ||||||||
\(534\) | −6.91540e11 | −0.368029 | ||||||||
\(535\) | −3.94755e10 | −0.0208322 | ||||||||
\(536\) | −2.37922e12 | −1.24507 | ||||||||
\(537\) | 5.43873e11 | 0.282236 | ||||||||
\(538\) | −3.69962e12 | −1.90387 | ||||||||
\(539\) | 2.58718e12 | 1.32031 | ||||||||
\(540\) | 1.27217e11 | 0.0643835 | ||||||||
\(541\) | 3.38496e12 | 1.69889 | 0.849445 | − | 0.527676i | \(-0.176937\pi\) | ||||
0.849445 | + | 0.527676i | \(0.176937\pi\) | |||||||
\(542\) | 2.23775e12 | 1.11382 | ||||||||
\(543\) | 7.99596e11 | 0.394704 | ||||||||
\(544\) | −1.15140e12 | −0.563676 | ||||||||
\(545\) | −8.44282e11 | −0.409924 | ||||||||
\(546\) | −2.98632e10 | −0.0143804 | ||||||||
\(547\) | 2.73500e12 | 1.30622 | 0.653108 | − | 0.757265i | \(-0.273465\pi\) | ||||
0.653108 | + | 0.757265i | \(0.273465\pi\) | |||||||
\(548\) | 5.24350e11 | 0.248376 | ||||||||
\(549\) | −1.39351e12 | −0.654687 | ||||||||
\(550\) | −3.07601e12 | −1.43336 | ||||||||
\(551\) | −1.90358e12 | −0.879810 | ||||||||
\(552\) | 1.57249e12 | 0.720877 | ||||||||
\(553\) | 5.10565e10 | 0.0232160 | ||||||||
\(554\) | −3.15907e12 | −1.42484 | ||||||||
\(555\) | −2.78174e11 | −0.124451 | ||||||||
\(556\) | 1.35456e11 | 0.0601122 | ||||||||
\(557\) | 4.19956e11 | 0.184865 | 0.0924326 | − | 0.995719i | \(-0.470536\pi\) | ||||
0.0924326 | + | 0.995719i | \(0.470536\pi\) | |||||||
\(558\) | −7.99477e11 | −0.349102 | ||||||||
\(559\) | 2.67800e11 | 0.116000 | ||||||||
\(560\) | 1.16435e11 | 0.0500307 | ||||||||
\(561\) | 2.08177e12 | 0.887361 | ||||||||
\(562\) | 9.21626e11 | 0.389710 | ||||||||
\(563\) | −4.08232e12 | −1.71245 | −0.856227 | − | 0.516600i | \(-0.827198\pi\) | ||||
−0.856227 | + | 0.516600i | \(0.827198\pi\) | |||||||
\(564\) | 2.70883e11 | 0.112726 | ||||||||
\(565\) | −2.89608e11 | −0.119562 | ||||||||
\(566\) | 1.16297e12 | 0.476315 | ||||||||
\(567\) | 2.41115e10 | 0.00979718 | ||||||||
\(568\) | −3.22300e12 | −1.29925 | ||||||||
\(569\) | 3.56221e12 | 1.42467 | 0.712334 | − | 0.701840i | \(-0.247638\pi\) | ||||
0.712334 | + | 0.701840i | \(0.247638\pi\) | |||||||
\(570\) | 2.18285e11 | 0.0866139 | ||||||||
\(571\) | −1.37253e12 | −0.540331 | −0.270166 | − | 0.962814i | \(-0.587078\pi\) | ||||
−0.270166 | + | 0.962814i | \(0.587078\pi\) | |||||||
\(572\) | −1.16793e11 | −0.0456179 | ||||||||
\(573\) | 1.54782e12 | 0.599825 | ||||||||
\(574\) | −6.95637e11 | −0.267472 | ||||||||
\(575\) | −3.58939e12 | −1.36935 | ||||||||
\(576\) | −1.04595e12 | −0.395923 | ||||||||
\(577\) | −4.32295e12 | −1.62364 | −0.811818 | − | 0.583911i | \(-0.801522\pi\) | ||||
−0.811818 | + | 0.583911i | \(0.801522\pi\) | |||||||
\(578\) | −5.93984e11 | −0.221360 | ||||||||
\(579\) | −2.41057e12 | −0.891388 | ||||||||
\(580\) | 3.03054e11 | 0.111197 | ||||||||
\(581\) | 2.00657e11 | 0.0730570 | ||||||||
\(582\) | −8.29955e10 | −0.0299848 | ||||||||
\(583\) | 5.91370e12 | 2.12007 | ||||||||
\(584\) | −7.25555e11 | −0.258115 | ||||||||
\(585\) | 5.76448e10 | 0.0203497 | ||||||||
\(586\) | 2.12870e12 | 0.745719 | ||||||||
\(587\) | 5.59187e11 | 0.194395 | 0.0971977 | − | 0.995265i | \(-0.469012\pi\) | ||||
0.0971977 | + | 0.995265i | \(0.469012\pi\) | |||||||
\(588\) | −4.43760e11 | −0.153091 | ||||||||
\(589\) | −7.31549e11 | −0.250452 | ||||||||
\(590\) | −1.13989e12 | −0.387282 | ||||||||
\(591\) | 1.26123e11 | 0.0425257 | ||||||||
\(592\) | −2.99360e12 | −1.00172 | ||||||||
\(593\) | −1.93158e12 | −0.641455 | −0.320728 | − | 0.947171i | \(-0.603927\pi\) | ||||
−0.320728 | + | 0.947171i | \(0.603927\pi\) | |||||||
\(594\) | −4.54794e12 | −1.49891 | ||||||||
\(595\) | 1.40113e11 | 0.0458302 | ||||||||
\(596\) | 3.93209e11 | 0.127648 | ||||||||
\(597\) | 1.69021e12 | 0.544575 | ||||||||
\(598\) | −6.52551e11 | −0.208670 | ||||||||
\(599\) | 6.61008e11 | 0.209791 | 0.104895 | − | 0.994483i | \(-0.466549\pi\) | ||||
0.104895 | + | 0.994483i | \(0.466549\pi\) | |||||||
\(600\) | −1.47103e12 | −0.463383 | ||||||||
\(601\) | −5.01901e12 | −1.56922 | −0.784608 | − | 0.619992i | \(-0.787136\pi\) | ||||
−0.784608 | + | 0.619992i | \(0.787136\pi\) | |||||||
\(602\) | −5.56914e11 | −0.172824 | ||||||||
\(603\) | 3.14465e12 | 0.968599 | ||||||||
\(604\) | 1.16613e12 | 0.356518 | ||||||||
\(605\) | −6.93529e11 | −0.210458 | ||||||||
\(606\) | 2.40026e12 | 0.722990 | ||||||||
\(607\) | 2.50351e12 | 0.748515 | 0.374257 | − | 0.927325i | \(-0.377898\pi\) | ||||
0.374257 | + | 0.927325i | \(0.377898\pi\) | |||||||
\(608\) | 9.01407e11 | 0.267519 | ||||||||
\(609\) | −5.78553e11 | −0.170438 | ||||||||
\(610\) | 9.71985e11 | 0.284233 | ||||||||
\(611\) | 3.13414e11 | 0.0909774 | ||||||||
\(612\) | 6.45202e11 | 0.185915 | ||||||||
\(613\) | −2.29177e12 | −0.655541 | −0.327770 | − | 0.944757i | \(-0.606297\pi\) | ||||
−0.327770 | + | 0.944757i | \(0.606297\pi\) | |||||||
\(614\) | 3.92469e12 | 1.11442 | ||||||||
\(615\) | −7.43132e11 | −0.209473 | ||||||||
\(616\) | −6.77180e11 | −0.189492 | ||||||||
\(617\) | 1.35559e12 | 0.376568 | 0.188284 | − | 0.982115i | \(-0.439707\pi\) | ||||
0.188284 | + | 0.982115i | \(0.439707\pi\) | |||||||
\(618\) | 1.74378e12 | 0.480889 | ||||||||
\(619\) | −9.06881e11 | −0.248280 | −0.124140 | − | 0.992265i | \(-0.539617\pi\) | ||||
−0.124140 | + | 0.992265i | \(0.539617\pi\) | |||||||
\(620\) | 1.16464e11 | 0.0316540 | ||||||||
\(621\) | −5.30699e12 | −1.43198 | ||||||||
\(622\) | 3.40686e12 | 0.912635 | ||||||||
\(623\) | 3.47510e11 | 0.0924211 | ||||||||
\(624\) | −3.43318e11 | −0.0906497 | ||||||||
\(625\) | 3.12207e12 | 0.818431 | ||||||||
\(626\) | −5.98503e12 | −1.55769 | ||||||||
\(627\) | −1.62978e12 | −0.421139 | ||||||||
\(628\) | 1.39614e12 | 0.358187 | ||||||||
\(629\) | −3.60238e12 | −0.917618 | ||||||||
\(630\) | −1.19877e11 | −0.0303183 | ||||||||
\(631\) | −3.64544e12 | −0.915415 | −0.457708 | − | 0.889103i | \(-0.651329\pi\) | ||||
−0.457708 | + | 0.889103i | \(0.651329\pi\) | |||||||
\(632\) | 4.57223e11 | 0.113999 | ||||||||
\(633\) | 4.33855e12 | 1.07406 | ||||||||
\(634\) | 6.50019e12 | 1.59781 | ||||||||
\(635\) | −6.91252e11 | −0.168715 | ||||||||
\(636\) | −1.01434e12 | −0.245824 | ||||||||
\(637\) | −5.13435e11 | −0.123554 | ||||||||
\(638\) | −1.08340e13 | −2.58878 | ||||||||
\(639\) | 4.25989e12 | 1.01075 | ||||||||
\(640\) | 1.27318e12 | 0.299971 | ||||||||
\(641\) | −3.45800e12 | −0.809029 | −0.404515 | − | 0.914531i | \(-0.632560\pi\) | ||||
−0.404515 | + | 0.914531i | \(0.632560\pi\) | |||||||
\(642\) | −2.42058e11 | −0.0562356 | ||||||||
\(643\) | 6.75236e12 | 1.55778 | 0.778890 | − | 0.627160i | \(-0.215783\pi\) | ||||
0.778890 | + | 0.627160i | \(0.215783\pi\) | |||||||
\(644\) | 2.83418e11 | 0.0649293 | ||||||||
\(645\) | −5.94937e11 | −0.135348 | ||||||||
\(646\) | 2.82682e12 | 0.638633 | ||||||||
\(647\) | −2.74120e12 | −0.614996 | −0.307498 | − | 0.951549i | \(-0.599492\pi\) | ||||
−0.307498 | + | 0.951549i | \(0.599492\pi\) | |||||||
\(648\) | 2.15924e11 | 0.0481077 | ||||||||
\(649\) | 8.51071e12 | 1.88306 | ||||||||
\(650\) | 6.10447e11 | 0.134134 | ||||||||
\(651\) | −2.22339e11 | −0.0485178 | ||||||||
\(652\) | −1.19995e12 | −0.260046 | ||||||||
\(653\) | −5.45651e11 | −0.117437 | −0.0587186 | − | 0.998275i | \(-0.518701\pi\) | ||||
−0.0587186 | + | 0.998275i | \(0.518701\pi\) | |||||||
\(654\) | −5.17701e12 | −1.10657 | ||||||||
\(655\) | −4.00043e11 | −0.0849220 | ||||||||
\(656\) | −7.99729e12 | −1.68607 | ||||||||
\(657\) | 9.58977e11 | 0.200800 | ||||||||
\(658\) | −6.51772e11 | −0.135544 | ||||||||
\(659\) | 2.20632e12 | 0.455704 | 0.227852 | − | 0.973696i | \(-0.426830\pi\) | ||||
0.227852 | + | 0.973696i | \(0.426830\pi\) | |||||||
\(660\) | 2.59464e11 | 0.0532268 | ||||||||
\(661\) | 9.47272e12 | 1.93005 | 0.965024 | − | 0.262161i | \(-0.0844353\pi\) | ||||
0.965024 | + | 0.262161i | \(0.0844353\pi\) | |||||||
\(662\) | 1.46903e12 | 0.297282 | ||||||||
\(663\) | −4.13136e11 | −0.0830389 | ||||||||
\(664\) | 1.79693e12 | 0.358736 | ||||||||
\(665\) | −1.09692e11 | −0.0217509 | ||||||||
\(666\) | 3.08211e12 | 0.607036 | ||||||||
\(667\) | −1.26422e13 | −2.47318 | ||||||||
\(668\) | 1.83565e12 | 0.356694 | ||||||||
\(669\) | −4.22117e11 | −0.0814733 | ||||||||
\(670\) | −2.19342e12 | −0.420519 | ||||||||
\(671\) | −7.25712e12 | −1.38201 | ||||||||
\(672\) | 2.73964e11 | 0.0518241 | ||||||||
\(673\) | −3.22229e12 | −0.605476 | −0.302738 | − | 0.953074i | \(-0.597901\pi\) | ||||
−0.302738 | + | 0.953074i | \(0.597901\pi\) | |||||||
\(674\) | −4.78680e12 | −0.893461 | ||||||||
\(675\) | 4.96457e12 | 0.920480 | ||||||||
\(676\) | −1.41012e12 | −0.259715 | ||||||||
\(677\) | −2.90840e11 | −0.0532115 | −0.0266057 | − | 0.999646i | \(-0.508470\pi\) | ||||
−0.0266057 | + | 0.999646i | \(0.508470\pi\) | |||||||
\(678\) | −1.77583e12 | −0.322751 | ||||||||
\(679\) | 4.17066e10 | 0.00752992 | ||||||||
\(680\) | 1.25474e12 | 0.225043 | ||||||||
\(681\) | −6.42613e11 | −0.114495 | ||||||||
\(682\) | −4.16352e12 | −0.736937 | ||||||||
\(683\) | −6.46343e12 | −1.13650 | −0.568250 | − | 0.822856i | \(-0.692379\pi\) | ||||
−0.568250 | + | 0.822856i | \(0.692379\pi\) | |||||||
\(684\) | −5.05117e11 | −0.0882348 | ||||||||
\(685\) | −1.34778e12 | −0.233890 | ||||||||
\(686\) | 2.16667e12 | 0.373538 | ||||||||
\(687\) | 3.22861e12 | 0.552980 | ||||||||
\(688\) | −6.40248e12 | −1.08943 | ||||||||
\(689\) | −1.17360e12 | −0.198396 | ||||||||
\(690\) | 1.44969e12 | 0.243475 | ||||||||
\(691\) | −1.94520e12 | −0.324573 | −0.162286 | − | 0.986744i | \(-0.551887\pi\) | ||||
−0.162286 | + | 0.986744i | \(0.551887\pi\) | |||||||
\(692\) | 1.87314e12 | 0.310522 | ||||||||
\(693\) | 8.95039e11 | 0.147415 | ||||||||
\(694\) | 2.23327e12 | 0.365447 | ||||||||
\(695\) | −3.48174e11 | −0.0566063 | ||||||||
\(696\) | −5.18108e12 | −0.836910 | ||||||||
\(697\) | −9.62362e12 | −1.54451 | ||||||||
\(698\) | −1.21971e13 | −1.94495 | ||||||||
\(699\) | 2.58596e12 | 0.409708 | ||||||||
\(700\) | −2.65131e11 | −0.0417369 | ||||||||
\(701\) | −5.04036e12 | −0.788370 | −0.394185 | − | 0.919031i | \(-0.628973\pi\) | ||||
−0.394185 | + | 0.919031i | \(0.628973\pi\) | |||||||
\(702\) | 9.02557e11 | 0.140268 | ||||||||
\(703\) | 2.82024e12 | 0.435499 | ||||||||
\(704\) | −5.44711e12 | −0.835775 | ||||||||
\(705\) | −6.96272e11 | −0.106152 | ||||||||
\(706\) | 1.51376e12 | 0.229317 | ||||||||
\(707\) | −1.20617e12 | −0.181561 | ||||||||
\(708\) | −1.45978e12 | −0.218343 | ||||||||
\(709\) | −1.12096e13 | −1.66602 | −0.833012 | − | 0.553255i | \(-0.813386\pi\) | ||||
−0.833012 | + | 0.553255i | \(0.813386\pi\) | |||||||
\(710\) | −2.97131e12 | −0.438819 | ||||||||
\(711\) | −6.04318e11 | −0.0886854 | ||||||||
\(712\) | 3.11203e12 | 0.453821 | ||||||||
\(713\) | −4.85840e12 | −0.704028 | ||||||||
\(714\) | 8.59151e11 | 0.123717 | ||||||||
\(715\) | 3.00203e11 | 0.0429574 | ||||||||
\(716\) | 8.77838e11 | 0.124826 | ||||||||
\(717\) | 5.38813e12 | 0.761381 | ||||||||
\(718\) | −1.68214e12 | −0.236212 | ||||||||
\(719\) | −9.06205e12 | −1.26458 | −0.632290 | − | 0.774732i | \(-0.717885\pi\) | ||||
−0.632290 | + | 0.774732i | \(0.717885\pi\) | |||||||
\(720\) | −1.37815e12 | −0.191118 | ||||||||
\(721\) | −8.76280e11 | −0.120763 | ||||||||
\(722\) | 5.99590e12 | 0.821177 | ||||||||
\(723\) | −5.01063e12 | −0.681977 | ||||||||
\(724\) | 1.29059e12 | 0.174568 | ||||||||
\(725\) | 1.18265e13 | 1.58977 | ||||||||
\(726\) | −4.25261e12 | −0.568121 | ||||||||
\(727\) | 7.11638e12 | 0.944832 | 0.472416 | − | 0.881376i | \(-0.343382\pi\) | ||||
0.472416 | + | 0.881376i | \(0.343382\pi\) | |||||||
\(728\) | 1.34389e11 | 0.0177326 | ||||||||
\(729\) | 4.18017e12 | 0.548176 | ||||||||
\(730\) | −6.68895e11 | −0.0871777 | ||||||||
\(731\) | −7.70449e12 | −0.997966 | ||||||||
\(732\) | 1.24476e12 | 0.160246 | ||||||||
\(733\) | −5.13324e12 | −0.656786 | −0.328393 | − | 0.944541i | \(-0.606507\pi\) | ||||
−0.328393 | + | 0.944541i | \(0.606507\pi\) | |||||||
\(734\) | −1.09882e13 | −1.39731 | ||||||||
\(735\) | 1.14063e12 | 0.144163 | ||||||||
\(736\) | 5.98647e12 | 0.752005 | ||||||||
\(737\) | 1.63767e13 | 2.04467 | ||||||||
\(738\) | 8.23374e12 | 1.02175 | ||||||||
\(739\) | 1.77858e12 | 0.219368 | 0.109684 | − | 0.993966i | \(-0.465016\pi\) | ||||
0.109684 | + | 0.993966i | \(0.465016\pi\) | |||||||
\(740\) | −4.48988e11 | −0.0550417 | ||||||||
\(741\) | 3.23436e11 | 0.0394101 | ||||||||
\(742\) | 2.44060e12 | 0.295582 | ||||||||
\(743\) | 1.21010e13 | 1.45671 | 0.728354 | − | 0.685201i | \(-0.240286\pi\) | ||||
0.728354 | + | 0.685201i | \(0.240286\pi\) | |||||||
\(744\) | −1.99110e12 | −0.238240 | ||||||||
\(745\) | −1.01070e12 | −0.120204 | ||||||||
\(746\) | −5.96445e12 | −0.705092 | ||||||||
\(747\) | −2.37503e12 | −0.279078 | ||||||||
\(748\) | 3.36009e12 | 0.392458 | ||||||||
\(749\) | 1.21638e11 | 0.0141222 | ||||||||
\(750\) | −2.80163e12 | −0.323321 | ||||||||
\(751\) | 1.05110e13 | 1.20577 | 0.602887 | − | 0.797827i | \(-0.294017\pi\) | ||||
0.602887 | + | 0.797827i | \(0.294017\pi\) | |||||||
\(752\) | −7.49300e12 | −0.854428 | ||||||||
\(753\) | −4.37021e12 | −0.495364 | ||||||||
\(754\) | 2.15005e12 | 0.242257 | ||||||||
\(755\) | −2.99740e12 | −0.335725 | ||||||||
\(756\) | −3.92001e11 | −0.0436455 | ||||||||
\(757\) | −7.38838e12 | −0.817745 | −0.408872 | − | 0.912592i | \(-0.634078\pi\) | ||||
−0.408872 | + | 0.912592i | \(0.634078\pi\) | |||||||
\(758\) | −4.35700e12 | −0.479376 | ||||||||
\(759\) | −1.08238e13 | −1.18383 | ||||||||
\(760\) | −9.82317e11 | −0.106805 | ||||||||
\(761\) | 7.44732e12 | 0.804950 | 0.402475 | − | 0.915431i | \(-0.368150\pi\) | ||||
0.402475 | + | 0.915431i | \(0.368150\pi\) | |||||||
\(762\) | −4.23865e12 | −0.455439 | ||||||||
\(763\) | 2.60153e12 | 0.277887 | ||||||||
\(764\) | 2.49826e12 | 0.265288 | ||||||||
\(765\) | −1.65841e12 | −0.175072 | ||||||||
\(766\) | 1.47164e13 | 1.54444 | ||||||||
\(767\) | −1.68898e12 | −0.176216 | ||||||||
\(768\) | 4.26767e12 | 0.442655 | ||||||||
\(769\) | −5.01390e12 | −0.517019 | −0.258510 | − | 0.966009i | \(-0.583231\pi\) | ||||
−0.258510 | + | 0.966009i | \(0.583231\pi\) | |||||||
\(770\) | −6.24298e11 | −0.0640005 | ||||||||
\(771\) | 3.04310e11 | 0.0310150 | ||||||||
\(772\) | −3.89079e12 | −0.394239 | ||||||||
\(773\) | −1.47690e13 | −1.48779 | −0.743896 | − | 0.668295i | \(-0.767024\pi\) | ||||
−0.743896 | + | 0.668295i | \(0.767024\pi\) | |||||||
\(774\) | 6.59178e12 | 0.660189 | ||||||||
\(775\) | 4.54492e12 | 0.452553 | ||||||||
\(776\) | 3.73492e11 | 0.0369746 | ||||||||
\(777\) | 8.57153e11 | 0.0843653 | ||||||||
\(778\) | −4.77458e12 | −0.467226 | ||||||||
\(779\) | 7.53416e12 | 0.733021 | ||||||||
\(780\) | −5.14917e10 | −0.00498094 | ||||||||
\(781\) | 2.21847e13 | 2.13365 | ||||||||
\(782\) | 1.87736e13 | 1.79522 | ||||||||
\(783\) | 1.74856e13 | 1.66247 | ||||||||
\(784\) | 1.22750e13 | 1.16038 | ||||||||
\(785\) | −3.58861e12 | −0.337297 | ||||||||
\(786\) | −2.45300e12 | −0.229243 | ||||||||
\(787\) | 2.41040e12 | 0.223977 | 0.111988 | − | 0.993710i | \(-0.464278\pi\) | ||||
0.111988 | + | 0.993710i | \(0.464278\pi\) | |||||||
\(788\) | 2.03569e11 | 0.0188081 | ||||||||
\(789\) | −8.81481e12 | −0.809779 | ||||||||
\(790\) | 4.21517e11 | 0.0385029 | ||||||||
\(791\) | 8.92384e11 | 0.0810508 | ||||||||
\(792\) | 8.01528e12 | 0.723862 | ||||||||
\(793\) | 1.44020e12 | 0.129329 | ||||||||
\(794\) | 1.73195e12 | 0.154648 | ||||||||
\(795\) | 2.60723e12 | 0.231487 | ||||||||
\(796\) | 2.72809e12 | 0.240852 | ||||||||
\(797\) | 1.86970e13 | 1.64138 | 0.820690 | − | 0.571374i | \(-0.193589\pi\) | ||||
0.820690 | + | 0.571374i | \(0.193589\pi\) | |||||||
\(798\) | −6.72614e11 | −0.0587155 | ||||||||
\(799\) | −9.01678e12 | −0.782692 | ||||||||
\(800\) | −5.60021e12 | −0.483392 | ||||||||
\(801\) | −4.11322e12 | −0.353050 | ||||||||
\(802\) | 8.16773e12 | 0.697135 | ||||||||
\(803\) | 4.99416e12 | 0.423880 | ||||||||
\(804\) | −2.80898e12 | −0.237081 | ||||||||
\(805\) | −7.28492e11 | −0.0611425 | ||||||||
\(806\) | 8.26266e11 | 0.0689624 | ||||||||
\(807\) | 1.21782e13 | 1.01077 | ||||||||
\(808\) | −1.08015e13 | −0.891528 | ||||||||
\(809\) | 5.77724e12 | 0.474189 | 0.237095 | − | 0.971487i | \(-0.423805\pi\) | ||||
0.237095 | + | 0.971487i | \(0.423805\pi\) | |||||||
\(810\) | 1.99062e11 | 0.0162483 | ||||||||
\(811\) | −2.29128e13 | −1.85987 | −0.929937 | − | 0.367719i | \(-0.880139\pi\) | ||||
−0.929937 | + | 0.367719i | \(0.880139\pi\) | |||||||
\(812\) | −9.33815e11 | −0.0753805 | ||||||||
\(813\) | −7.36609e12 | −0.591329 | ||||||||
\(814\) | 1.60510e13 | 1.28143 | ||||||||
\(815\) | 3.08434e12 | 0.244879 | ||||||||
\(816\) | 9.87711e12 | 0.779874 | ||||||||
\(817\) | 6.03171e12 | 0.473632 | ||||||||
\(818\) | −2.63182e13 | −2.05526 | ||||||||
\(819\) | −1.77624e11 | −0.0137951 | ||||||||
\(820\) | −1.19945e12 | −0.0926447 | ||||||||
\(821\) | −1.20930e13 | −0.928944 | −0.464472 | − | 0.885588i | \(-0.653756\pi\) | ||||
−0.464472 | + | 0.885588i | \(0.653756\pi\) | |||||||
\(822\) | −8.26437e12 | −0.631374 | ||||||||
\(823\) | 1.45424e13 | 1.10493 | 0.552467 | − | 0.833535i | \(-0.313687\pi\) | ||||
0.552467 | + | 0.833535i | \(0.313687\pi\) | |||||||
\(824\) | −7.84729e12 | −0.592990 | ||||||||
\(825\) | 1.01254e13 | 0.760974 | ||||||||
\(826\) | 3.51239e12 | 0.262538 | ||||||||
\(827\) | −1.27869e13 | −0.950584 | −0.475292 | − | 0.879828i | \(-0.657658\pi\) | ||||
−0.475292 | + | 0.879828i | \(0.657658\pi\) | |||||||
\(828\) | −3.35461e12 | −0.248031 | ||||||||
\(829\) | 2.02455e13 | 1.48879 | 0.744394 | − | 0.667741i | \(-0.232739\pi\) | ||||
0.744394 | + | 0.667741i | \(0.232739\pi\) | |||||||
\(830\) | 1.65660e12 | 0.121162 | ||||||||
\(831\) | 1.03988e13 | 0.756448 | ||||||||
\(832\) | 1.08100e12 | 0.0782116 | ||||||||
\(833\) | 1.47713e13 | 1.06296 | ||||||||
\(834\) | −2.13495e12 | −0.152806 | ||||||||
\(835\) | −4.71832e12 | −0.335891 | ||||||||
\(836\) | −2.63055e12 | −0.186260 | ||||||||
\(837\) | 6.71975e12 | 0.473248 | ||||||||
\(838\) | 2.10280e13 | 1.47299 | ||||||||
\(839\) | −1.34126e13 | −0.934509 | −0.467254 | − | 0.884123i | \(-0.654757\pi\) | ||||
−0.467254 | + | 0.884123i | \(0.654757\pi\) | |||||||
\(840\) | −2.98555e11 | −0.0206903 | ||||||||
\(841\) | 2.71467e13 | 1.87126 | ||||||||
\(842\) | −1.79150e13 | −1.22832 | ||||||||
\(843\) | −3.03374e12 | −0.206897 | ||||||||
\(844\) | 7.00265e12 | 0.475030 | ||||||||
\(845\) | 3.62455e12 | 0.244568 | ||||||||
\(846\) | 7.71455e12 | 0.517778 | ||||||||
\(847\) | 2.13701e12 | 0.142669 | ||||||||
\(848\) | 2.80580e13 | 1.86327 | ||||||||
\(849\) | −3.82818e12 | −0.252876 | ||||||||
\(850\) | −1.75623e13 | −1.15397 | ||||||||
\(851\) | 1.87299e13 | 1.22420 | ||||||||
\(852\) | −3.80518e12 | −0.247399 | ||||||||
\(853\) | 2.07726e13 | 1.34344 | 0.671722 | − | 0.740803i | \(-0.265555\pi\) | ||||
0.671722 | + | 0.740803i | \(0.265555\pi\) | |||||||
\(854\) | −2.99503e12 | −0.192682 | ||||||||
\(855\) | 1.29834e12 | 0.0830887 | ||||||||
\(856\) | 1.08930e12 | 0.0693448 | ||||||||
\(857\) | 1.47520e13 | 0.934192 | 0.467096 | − | 0.884207i | \(-0.345300\pi\) | ||||
0.467096 | + | 0.884207i | \(0.345300\pi\) | |||||||
\(858\) | 1.84080e12 | 0.115961 | ||||||||
\(859\) | 1.11817e13 | 0.700711 | 0.350356 | − | 0.936617i | \(-0.386061\pi\) | ||||
0.350356 | + | 0.936617i | \(0.386061\pi\) | |||||||
\(860\) | −9.60260e11 | −0.0598612 | ||||||||
\(861\) | 2.28985e12 | 0.142001 | ||||||||
\(862\) | −7.00725e12 | −0.432280 | ||||||||
\(863\) | −1.23584e13 | −0.758428 | −0.379214 | − | 0.925309i | \(-0.623806\pi\) | ||||
−0.379214 | + | 0.925309i | \(0.623806\pi\) | |||||||
\(864\) | −8.28002e12 | −0.505498 | ||||||||
\(865\) | −4.81467e12 | −0.292412 | ||||||||
\(866\) | −2.56692e10 | −0.00155089 | ||||||||
\(867\) | 1.95523e12 | 0.117520 | ||||||||
\(868\) | −3.58866e11 | −0.0214582 | ||||||||
\(869\) | −3.14717e12 | −0.187211 | ||||||||
\(870\) | −4.77648e12 | −0.282665 | ||||||||
\(871\) | −3.25002e12 | −0.191339 | ||||||||
\(872\) | 2.32973e13 | 1.36453 | ||||||||
\(873\) | −4.93650e11 | −0.0287644 | ||||||||
\(874\) | −1.46975e13 | −0.852005 | ||||||||
\(875\) | 1.40786e12 | 0.0811940 | ||||||||
\(876\) | −8.56614e11 | −0.0491492 | ||||||||
\(877\) | 1.39608e13 | 0.796917 | 0.398459 | − | 0.917186i | \(-0.369545\pi\) | ||||
0.398459 | + | 0.917186i | \(0.369545\pi\) | |||||||
\(878\) | −2.09676e13 | −1.19076 | ||||||||
\(879\) | −7.00711e12 | −0.395903 | ||||||||
\(880\) | −7.17715e12 | −0.403441 | ||||||||
\(881\) | −1.27684e13 | −0.714079 | −0.357039 | − | 0.934089i | \(-0.616214\pi\) | ||||
−0.357039 | + | 0.934089i | \(0.616214\pi\) | |||||||
\(882\) | −1.26380e13 | −0.703183 | ||||||||
\(883\) | 8.68951e12 | 0.481030 | 0.240515 | − | 0.970645i | \(-0.422684\pi\) | ||||
0.240515 | + | 0.970645i | \(0.422684\pi\) | |||||||
\(884\) | −6.66822e11 | −0.0367261 | ||||||||
\(885\) | 3.75220e12 | 0.205608 | ||||||||
\(886\) | 3.67894e13 | 2.00572 | ||||||||
\(887\) | 8.63030e11 | 0.0468133 | 0.0234067 | − | 0.999726i | \(-0.492549\pi\) | ||||
0.0234067 | + | 0.999726i | \(0.492549\pi\) | |||||||
\(888\) | 7.67601e12 | 0.414264 | ||||||||
\(889\) | 2.12999e12 | 0.114372 | ||||||||
\(890\) | 2.86901e12 | 0.153277 | ||||||||
\(891\) | −1.48626e12 | −0.0790031 | ||||||||
\(892\) | −6.81319e11 | −0.0360337 | ||||||||
\(893\) | 7.05908e12 | 0.371464 | ||||||||
\(894\) | −6.19744e12 | −0.324484 | ||||||||
\(895\) | −2.25638e12 | −0.117546 | ||||||||
\(896\) | −3.92311e12 | −0.203350 | ||||||||
\(897\) | 2.14802e12 | 0.110783 | ||||||||
\(898\) | 5.51175e12 | 0.282844 | ||||||||
\(899\) | 1.60076e13 | 0.817350 | ||||||||
\(900\) | 3.13816e12 | 0.159435 | ||||||||
\(901\) | 3.37639e13 | 1.70683 | ||||||||
\(902\) | 4.28797e13 | 2.15686 | ||||||||
\(903\) | 1.83321e12 | 0.0917524 | ||||||||
\(904\) | 7.99151e12 | 0.397989 | ||||||||
\(905\) | −3.31730e12 | −0.164387 | ||||||||
\(906\) | −1.83796e13 | −0.906272 | ||||||||
\(907\) | −7.79700e12 | −0.382556 | −0.191278 | − | 0.981536i | \(-0.561263\pi\) | ||||
−0.191278 | + | 0.981536i | \(0.561263\pi\) | |||||||
\(908\) | −1.03721e12 | −0.0506385 | ||||||||
\(909\) | 1.42766e13 | 0.693563 | ||||||||
\(910\) | 1.23894e11 | 0.00598915 | ||||||||
\(911\) | −3.57204e13 | −1.71824 | −0.859120 | − | 0.511774i | \(-0.828988\pi\) | ||||
−0.859120 | + | 0.511774i | \(0.828988\pi\) | |||||||
\(912\) | −7.73261e12 | −0.370126 | ||||||||
\(913\) | −1.23687e13 | −0.589122 | ||||||||
\(914\) | 1.83424e13 | 0.869356 | ||||||||
\(915\) | −3.19951e12 | −0.150900 | ||||||||
\(916\) | 5.21114e12 | 0.244570 | ||||||||
\(917\) | 1.23267e12 | 0.0575686 | ||||||||
\(918\) | −2.59662e13 | −1.20675 | ||||||||
\(919\) | −1.55458e12 | −0.0718939 | −0.0359470 | − | 0.999354i | \(-0.511445\pi\) | ||||
−0.0359470 | + | 0.999354i | \(0.511445\pi\) | |||||||
\(920\) | −6.52381e12 | −0.300232 | ||||||||
\(921\) | −1.29190e13 | −0.591645 | ||||||||
\(922\) | 4.97315e12 | 0.226643 | ||||||||
\(923\) | −4.40264e12 | −0.199666 | ||||||||
\(924\) | −7.99501e11 | −0.0360824 | ||||||||
\(925\) | −1.75214e13 | −0.786922 | ||||||||
\(926\) | −3.77265e13 | −1.68615 | ||||||||
\(927\) | 1.03719e13 | 0.461316 | ||||||||
\(928\) | −1.97244e13 | −0.873049 | ||||||||
\(929\) | 2.73767e13 | 1.20590 | 0.602948 | − | 0.797781i | \(-0.293993\pi\) | ||||
0.602948 | + | 0.797781i | \(0.293993\pi\) | |||||||
\(930\) | −1.83561e12 | −0.0804649 | ||||||||
\(931\) | −1.15642e13 | −0.504477 | ||||||||
\(932\) | 4.17387e12 | 0.181204 | ||||||||
\(933\) | −1.12145e13 | −0.484519 | ||||||||
\(934\) | 2.93006e13 | 1.25984 | ||||||||
\(935\) | −8.63670e12 | −0.369569 | ||||||||
\(936\) | −1.59066e12 | −0.0677388 | ||||||||
\(937\) | −3.01208e13 | −1.27655 | −0.638276 | − | 0.769808i | \(-0.720352\pi\) | ||||
−0.638276 | + | 0.769808i | \(0.720352\pi\) | |||||||
\(938\) | 6.75870e12 | 0.285069 | ||||||||
\(939\) | 1.97011e13 | 0.826981 | ||||||||
\(940\) | −1.12382e12 | −0.0469484 | ||||||||
\(941\) | −3.77327e13 | −1.56879 | −0.784395 | − | 0.620261i | \(-0.787027\pi\) | ||||
−0.784395 | + | 0.620261i | \(0.787027\pi\) | |||||||
\(942\) | −2.20048e13 | −0.910517 | ||||||||
\(943\) | 5.00362e13 | 2.06054 | ||||||||
\(944\) | 4.03797e13 | 1.65497 | ||||||||
\(945\) | 1.00759e12 | 0.0411000 | ||||||||
\(946\) | 3.43287e13 | 1.39363 | ||||||||
\(947\) | −2.42971e13 | −0.981703 | −0.490852 | − | 0.871243i | \(-0.663314\pi\) | ||||
−0.490852 | + | 0.871243i | \(0.663314\pi\) | |||||||
\(948\) | 5.39812e11 | 0.0217073 | ||||||||
\(949\) | −9.91111e11 | −0.0396666 | ||||||||
\(950\) | 1.37492e13 | 0.547672 | ||||||||
\(951\) | −2.13969e13 | −0.848278 | ||||||||
\(952\) | −3.86631e12 | −0.152556 | ||||||||
\(953\) | 3.11007e13 | 1.22138 | 0.610691 | − | 0.791869i | \(-0.290892\pi\) | ||||
0.610691 | + | 0.791869i | \(0.290892\pi\) | |||||||
\(954\) | −2.88876e13 | −1.12913 | ||||||||
\(955\) | −6.42148e12 | −0.249816 | ||||||||
\(956\) | 8.69672e12 | 0.336740 | ||||||||
\(957\) | 3.56626e13 | 1.37439 | ||||||||
\(958\) | −3.21926e13 | −1.23484 | ||||||||
\(959\) | 4.15298e12 | 0.158554 | ||||||||
\(960\) | −2.40152e12 | −0.0912569 | ||||||||
\(961\) | −2.02879e13 | −0.767328 | ||||||||
\(962\) | −3.18539e12 | −0.119915 | ||||||||
\(963\) | −1.43974e12 | −0.0539468 | ||||||||
\(964\) | −8.08742e12 | −0.301622 | ||||||||
\(965\) | 1.00008e13 | 0.371246 | ||||||||
\(966\) | −4.46700e12 | −0.165051 | ||||||||
\(967\) | 1.88582e13 | 0.693554 | 0.346777 | − | 0.937948i | \(-0.387276\pi\) | ||||
0.346777 | + | 0.937948i | \(0.387276\pi\) | |||||||
\(968\) | 1.91374e13 | 0.700557 | ||||||||
\(969\) | −9.30512e12 | −0.339051 | ||||||||
\(970\) | 3.44325e11 | 0.0124881 | ||||||||
\(971\) | −2.84505e13 | −1.02708 | −0.513539 | − | 0.858066i | \(-0.671666\pi\) | ||||
−0.513539 | + | 0.858066i | \(0.671666\pi\) | |||||||
\(972\) | 7.46257e12 | 0.268158 | ||||||||
\(973\) | 1.07285e12 | 0.0383734 | ||||||||
\(974\) | −2.79219e12 | −0.0994099 | ||||||||
\(975\) | −2.00943e12 | −0.0712117 | ||||||||
\(976\) | −3.44319e13 | −1.21461 | ||||||||
\(977\) | −1.03143e13 | −0.362172 | −0.181086 | − | 0.983467i | \(-0.557961\pi\) | ||||
−0.181086 | + | 0.983467i | \(0.557961\pi\) | |||||||
\(978\) | 1.89127e13 | 0.661040 | ||||||||
\(979\) | −2.14208e13 | −0.745271 | ||||||||
\(980\) | 1.84104e12 | 0.0637596 | ||||||||
\(981\) | −3.07924e13 | −1.06153 | ||||||||
\(982\) | −5.59559e13 | −1.92019 | ||||||||
\(983\) | −9.89411e12 | −0.337976 | −0.168988 | − | 0.985618i | \(-0.554050\pi\) | ||||
−0.168988 | + | 0.985618i | \(0.554050\pi\) | |||||||
\(984\) | 2.05061e13 | 0.697278 | ||||||||
\(985\) | −5.23251e11 | −0.0177111 | ||||||||
\(986\) | −6.18558e13 | −2.08418 | ||||||||
\(987\) | 2.14546e12 | 0.0719603 | ||||||||
\(988\) | 5.22043e11 | 0.0174301 | ||||||||
\(989\) | 4.00581e13 | 1.33139 | ||||||||
\(990\) | 7.38935e12 | 0.244483 | ||||||||
\(991\) | −4.83417e13 | −1.59217 | −0.796087 | − | 0.605182i | \(-0.793100\pi\) | ||||
−0.796087 | + | 0.605182i | \(0.793100\pi\) | |||||||
\(992\) | −7.58012e12 | −0.248527 | ||||||||
\(993\) | −4.83565e12 | −0.157828 | ||||||||
\(994\) | 9.15566e12 | 0.297475 | ||||||||
\(995\) | −7.01224e12 | −0.226805 | ||||||||
\(996\) | 2.12151e12 | 0.0683092 | ||||||||
\(997\) | 2.17418e13 | 0.696894 | 0.348447 | − | 0.937329i | \(-0.386709\pi\) | ||||
0.348447 | + | 0.937329i | \(0.386709\pi\) | |||||||
\(998\) | 6.34125e13 | 2.02343 | ||||||||
\(999\) | −2.59058e13 | −0.822909 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 197.10.a.b.1.20 | ✓ | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.10.a.b.1.20 | ✓ | 76 | 1.1 | even | 1 | trivial |